ASSESSMENT AND STRATEGIES FOR TEACHING NUMERACY

1 ASSESSMENT AND. STRATEGIES FOR. TEACHING NUMERACY . Including Pupils with NUMERACY Difficulties The Highland Council Psychological Service January 2017. The Highland Council Psychological Service (THCPS). 1. CONTENTS. INTRODUCTION .. 3. National Context .. 3. Local Context .. 3. DEFINITIONS AND IDENTIFICATION .. 4. The Nature of NUMERACY and Maths .. 4. A Specific Difficulty in Maths (known previously as Dyscalculia).. 5. FEATURES OF PERSISTENT DIFFICULTIES WITH NUMERACY .. 5. Number 5. Remembering facts about NUMERACY and maths .. 6. Visuo-Spatial .. 6. Maths Anxiety .. 6. LEARNING AND TEACHING .. 6. Gathering ASSESSMENT Information .. 7. Classroom ASSESSMENT and Monitoring (Stage 1) .. 7. Contextual ASSESSMENT Information (Stage 1, possibly Stage 2).. 7. Individual ASSESSMENT to Identify Barriers to Learning (Stage 2) .. 8. Intervention.

2 9. Learning Environment (Universal Intervention, Stage 1) .. 9. TEACHING (Universal and Targeted Intervention, Stage 1 and 2) .. 9. Challenge (Universal and Targeted Intervention, Stage 1 and 2) .. 10. Evaluating Progress and Next Steps .. 11. Evaluation for Improvement (Stage 1, 2 and 3).. 11. Role of Specialist Professionals in Learning and TEACHING (Stage 3 and 4) .. 11. Role of an Educational Psychologist in Learning and TEACHING .. 11. Role of Other Allied Professionals in Learning and TEACHING .. 12. REFERENCES .. 13. Appendix A: Template (proforma) for reporting persistent difficulties with NUMERACY ASSESSMENT .. 15. Appendix B: A Staged Approach to Identifying and Responding to Additional Support Needs .. 21. Appendix C: Tables of Difficulties Associated with Learning NUMERACY .. 22. Appendix D: Persistent Difficulties with NUMERACY and Additional Support 26.

3 Appendix E: Scottish Qualifications Authority (SQA) and ASSESSMENT Arrangements .. 29. Appendix F: Suggested Support Materials for Classroom Use: Annotated Bibliography .. 31. Appendix G: Acknowledgements .. 34. The Highland Council Psychological Service (THCPS). 2. INTRODUCTION. The purpose of this practice paper is to outline The Highland Council Psychological Service (THCPS). approach to meeting the needs of children and young people learning NUMERACY , including those with persistent difficulties with NUMERACY . The aim is to address an expressed need from schools for more guidance regarding identification and intervention for pupils experiencing persistent difficulties with NUMERACY . In this practice paper, the focus is mainly on difficulties with NUMERACY : basic number knowledge and arithmetical procedures. Wider mathematical concepts ( shape, geometry, algebra etc.)

4 Are referred to but not discussed at length. Difficulties with NUMERACY can be attributed to a variety of causes (see Appendix D for further discussion about Additional Support Needs) and may not be due to a specific learning difficulty. For these reasons, the authors have used the description Persistent Difficulties with NUMERACY ', as discussed further in the definition section. National Context Raising the standards of educational attainment for all, in the core skills of literacy and NUMERACY , is a National Priority (The Education (National Priorities) (Scotland) Order 2000). This was emphasised in the Raising Attainment for All programme that was launched in 2014 by the Scottish Government. Curriculum for Excellence (SEED, 2009) stated that NUMERACY and literacy deserved equal time and weighting of importance. NUMERACY Hubs (introduced in 2014) have raised the profile of maths TEACHING and professional development.

5 Local Context The aim of the Highland NUMERACY Strategy is to ensure that all young people develop the NUMERACY skills they need to achieve success in life, learning and work (Highland Council, 2016, ,). The authority aims to increase shared understanding amongst staff about development of NUMERACY to support practitioners in planning and integrating learning, TEACHING and ASSESSMENT through Professional Learning, The Highland NUMERACY Blog and The Highland NUMERACY Progression (Highland Council, 2016, ,). THCPS is part of this strategy and is represented on the NUMERACY Steering Group. We have been tasked to focus on ASSESSMENT and intervention for learners, including those with persistent difficulties with NUMERACY . The Highland NUMERACY Progression is based on the Maths Recovery programme and New Zealand Maths. Maths Recovery is an evidence-based intensive intervention, underpinned by the Stages of Early Arithmetical Learning (Wright, Martland & Stafford, 2006).

6 New Zealand Maths is a universal programme, used in some Highland Schools. The content and STRATEGIES from these programmes was mapped onto Curriculum for Excellence Levels, appropriate Experiences and Outcomes, and Significant Aspects of Learning making it suitable for a Scottish Context. It is designed to be a guide for planning, a reference document and a key resource for TEACHING NUMERACY and maths (Highland Council, 2016). The ASSESSMENT guidance in this practice paper is based upon The Highland NUMERACY Progression and the associated Diagnostic Assessments. These resources are available from The Highland NUMERACY Blog alongside training for their use. The Highland Council Psychological Service (THCPS). 3. DEFINITIONS AND IDENTIFICATION. The Nature of NUMERACY and Maths Learners develop competence and confidence in NUMERACY by learning facts about numbers ( how quantities are represented in different ways etc.)

7 , how numbers represent quantity in the real world and how numbers interact through learning procedures ( adding numbers together etc.). The knowledge and skills then have to be applied in a logical and reasoned way in order to make sense of the world and once that is achieved then an individual is numerate (Emerson & Babtie, 2013). In Curriculum for Excellence, learners are considered numerate if they have developed the confidence and competence in using number which will allow individuals to solve problems, analyse information and make informed decisions based on calculations. (Scottish Government, 2009, ,). The essential knowledge and skills required to become numerate are: accurate counting; remembering key number facts; logical reasoning and problem solving ability (Emerson & Babtie, 2013). The foundation of NUMERACY is counting which is a set of skills and knowledge that takes years to master fully in normal development.

8 All the principles listed below must be applied to count fluently (see Figure 1): Recitation One to one one (learning the correspondence number words and (each item gets one the ability to recite and only one them in a count). One two three . two sequence). Stable ordering Cardinality (the number One two three (the quantity being One, two, words are always represented, the three, four, said in the same last word in the five, six order) count represents the cardinality of there are three items the set). Order irrelevance Item kind three one two (items can be One two three irrelevance, or counted in any abstraction order) (refers to no restrictions on countable entities, there are still three Three various items anything can be items counted together). Figure 1: Counting principles diagrams (Gelman & Gallistel, cited in Cordes & Gelman, 2005; Emerson &.)

9 Babtie, 2013; Sullivan et al., 2005). The Highland Council Psychological Service (THCPS). 4. NUMERACY activities, even in the earliest stages, involve a wide variety of facts, the language used, abstract concepts (numbers as internal representations of quantity) and complex mental activities (comparisons and calculation procedures). It can take a long time to become secure with the knowledge and skills required, because they need to be reinforced and understood. The knowledge and skills are progressive, building on each other. Children tend to learn to count and sequence numbers before learning to add and subtract, then move on to learning multiplication, division and so on (for example). If learners experience difficulty acquiring the required knowledge or skills due to anxiety, behavioural difficulties, inappropriate TEACHING , disrupted education or learning difficulties then they could struggle to progress and may perform poorly (Butterworth, 2005).

10 Learning difficulties specifically refer to difficulties with cognitive skills that affect learning including difficulties with attention, concentration, memory (short-term, long-term and/or working memory), reasoning and sequencing (APA, 2013; Emerson & Babtie, 2013). A Specific Difficulty in Maths (known previously as Dyscalculia). There are various reasons why a person may experience difficulties with NUMERACY and perform poorly in mathematical tasks and only a small proportion will be due to a specific learning difficulty in maths, sometimes referred to as dyscalculia, ( Butterworth, 2005; Emerson & Babtie, 2013). At the time of writing (January 2017), there was no longer any reference to the term dyscalculia' on the Education Scotland website, or on the Department for Education website (BDA, 2015) which had a widely published definition from 2001, ( Butterworth, 2005; Butterworth & Yeo, 2004; Emerson &.)